Overview

The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and hence gives the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Thangavelu's exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable.

Full Product Details

Author:   Sundaram Thangavelu
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1998
Volume:   159
Dimensions:   Width: 15.50cm , Height: 1.10cm , Length: 23.50cm
Weight:   0.332kg
ISBN:  

9781461272755

ISBN 10:   1461272750
Pages:   195
Publication Date:   08 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

1 The Group Fourier Transform.- 1.1 The Heisenberg group.- 1.2 The Schrödinger representations.- 1.3 The Fourier and Weyl transforms.- 1.4 Hermite and special Hermite functions.- 1.5 Paley—Wiener theorems for the Fourier transform.- 1.6 An uncertainty principle on the Heisenberg group.- 1.7 Notes and references.- 2 Analysis of the Sublaplacian.- 2.1 Spectral theory of the sublaplacian.- 2.2 Spectral decomposition for Lp functions.- 2.3 Restriction theorems for the spectral projections.- 2.4 A Paley-Wiener theorem for the spectral projections.- 2.5 Bochner-Riesz means for the sublaplacian.- 2.6 A multiplier theorem for the Fourier transform.- 2.7 Notes and references.- 3 Group Algebras and Applications.- 3.1 The Heisenberg motion group.- 3.2 Gelfand pairs, spherical functions and group algebras.- 3.3 An algebra of radial measures.- 3.4 Analogues of Wiener-Tauberian theorem.- 3.5 Spherical means on the Heisenberg group.- 3.6 A maximal theorem for spherical means.- 3.7 Notes and references.- 4 The Reduced Heisenberg Group.- 4.1 The reduced Heisenberg group.- 4.2 A Wiener-Tauberian theorem for Lp functions.- 4.3 A maximal theorem for spherical means.- 4.4 Mean periodic functions on phase space.- 4.5 Notes and references.

Reviews

The author is to be commended for assembling this diverse body of interesting results into a coherent and readable monograph...Thangavelu's work....gives a useful survey of the field, bringing together a number of recent results which have not appeared elsewhere in book form and which will appeal to a broad mathematical audience... -Mathematical Reviews

The author is to be commended for assembling this diverse body of interesting results into a coherent and readable monograph...Thangavelu's work...gives a useful survey of the field, bringing together a number of recent results which have not appeared elsewhere in book form and which will appeal to a broad mathematical audience... -Mathematical Reviews

The author is to be commended for assembling this diverse body of interesting results into a coherent and readable monograph...Thangavelu's work....gives a useful survey of the field, bringing together a number of recent results which have not appeared elsewhere in book form and which will appeal to a broad mathematical audience... -Mathematical Reviews

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